2018 CHS - Sec 4 Math Prelim Exam P1 - QUESTION PAPER AND ANS

1 CHS Preliminary Examination 2018 [TURN OVER Name: Index Number: Class: CATHOLIC HIGH SCHOOL Preliminary Examination Secondary 4 (O-Level Programme) MATHEMATICS 4048/01 Paper 1 113 SEPTEMBER 2018 2 hours Candidates answer in the space provided on the Question Paper. READ THESE INSTRUCTIONS FIRST Write your name, register number and class on all the work you hand in. Write in dark blue or black pen. You may use a soft pencil for any diagrams or graphs. Do not use staples, paper clips, highlighters, glue or correction fluid. DO NOT WRITE ON THE MARGINS. Answer all questions. If working is needed for any question, it must be shown with the answer. Omission of essential working will result in loss of marks. The use of an approved scientific calculator is expected, where appropriate. If the degree of accuracy is not specified in the question, and if the answer is not exact, give the answer to three significant figures. Give answers in degrees to one decimal place. For  , use either your calculator value or 3.142, unless the question requires the answer in terms of  . At the end of the examination, fasten all your work securely together. The number of marks is given in brackets [ ] at the end of each question or part question. The total of the marks for this paper is 80. This document consists of 23 printed pages. For Examiner’s Use only 80

2 CHS Preliminary Examination 2018 [TURN OVER Mathematical Formulae Compound interest Total amount = nrP       1001 Mensuration Curved surface area of a cone = lr  Surface area of a sphere = 2 4 r Volume of a cone = hr 3 1 2 Volume of a sphere = 3 3 4 r Area of triangle ABC = Cba sin 2 1 Arc length = r , where  is in radians Sector area = 2 2 1 r , where  is in radians Trigonometry C c B b A a sin sin sin  Acbcba cos 2 222  Statistics Mean =   f xf Standard deviation = 22           f xf f xf

3 CHS Preliminary Examination 2018 [TURN OVER Answer all the questions. 1 Given that   1 233 27 9 x  , find the value of x. Answer x = [1] 2 A conical container has base radius of 5.8 cm and a capacity of 1.2 litres. Calculate the height of the container. Answer cm [1]

4 CHS Preliminary Examination 2018 [TURN OVER 3 14 men were hired to work 8 hours per day to complete a renovation job in 20 days. At the end of the 3 rd day, x workers became sick and were hospitalised. Assume that all workers work at the same rate. On average, how many hours must each of the remaining men work for the remaining days in order to complete the job? Leave your answer in terms of x. Answer hours [2] 4 Find the sum of the angles a, b, c, d, e, f and g. Answer  [2] a f e c d g b

5 CHS Preliminary Examination 2018 [TURN OVER 5 (a) The intensity of radiation, p units, is inversely proportional to the square of the distance, h metres, from a radioactive source. Find the percentage change in radiation when the distance is decreased by 20%. Answer % [2] (b) The cost, $T, of supplying x units of electricity to a household are given in the table below. No. of units used, x 100 200 500 1 000 Total cost, $T 22 27 42 67 Showing your working clearly, determine if T is directly proportional to x. [2]

6 CHS Preliminary Examination 2018 [TURN OVER 6 A certain number is 3 2 5 x  when it is written as a product of its prime factors. (a) Write down the value of x if 3 2 5 2000 x   . Answer x = [1] (b) State the condition of x if this number is to be a perfect cube. Answer [1] 7 The diagram shows a straight line with equation y mx , passing through the point  2 ,g g . (i) State the value of m. Answer m = [1] (ii) Using the value of m found in (i), sketch the graph of 2y mx g  in the diagram above. Label all intercepts clearly. [1] y x 2g O g

7 CHS Preliminary Examination 2018 [TURN OVER 8 A map is drawn to a scale of 1 : 50 000. (a) An airport runway is represented by a line of length 5.8 cm on the map. Calculate the actual length of the runway, giving your answer in kilometres. Answer km [1] (b) The area of the airport on the map is 50 cm2. Calculate the area in cm2 which represents the same airport on a second map whose scale is 1 : 40 000. Answer cm2 [2]

8 CHS Preliminary Examination 2018 [TURN OVER 9 The two jars are geometrically similar. The height of the smaller container is 14 cm. The height of the larger container is 22 cm. (a) The mouth of the larger con tainer has a circumference of 55 cm. Find the circumference of the mouth of the smaller container. Answer cm [1] (b) Both containers are completely filled with water. The smaller container can hold 1 litre of water. Find the volume of water in the larger container, giving your answer correct to the nearest cm3. Answer cm3 [2] 22 cm 14 cm

9 CHS Preliminary Examination 2018 [TURN OVER 10 Solve the following simultaneous equations. 111.5 14 3 56 7 3 x y x y     Answer x = y = [3]

10 CHS Preliminary Examination 2018 [TURN OVER 11 The diagram shows the graph of   y a x b x c   . The line 10y  cuts the curve at 4x and 2x and the curve cuts the y-axis at 6y . Find the values of a, b and c, where a, b and c are positive integers. Answer a = b = c = [5] 0 2 – 4 x y – 6